Heat a medium Dutch oven over medium-high heat and add 2 tablespoons of the oil. Add the leeks and salt and cook, stirring often, until the leeks are very soft, about 5 minutes. Add the potatoes and stir to combine. Cook for an additional 2 minutes to let the flavors marry. Stir in the chicken broth and pepper flakes. Add the cheese rind and bring to a simmer. Reduce the heat to medium low to maintain a gentle simmer and cook until the potatoes are tender, about 20 minutes. Stir in the arugula and cook until wilted, about 1 minute. Remove from the heat and discard the cheese rind.
Add the remaining 1/4 cup olive oil and the lemon juice. Using a handheld blender, puree until completely smooth. Ladle into bowls or cups and top evenly with the mascarpone.